Abstract

We present the theoretical and simulation results of the relationship between three input states of polarization (SOP) and the Mueller matrix measurement error in an optical system having birefringence and finite polarization-dependent loss or gain (PDL/G). By using the condition number as the criterion, it can be theoretically demonstrated that the three input SOPs should be equally-spaced on the Poincaré sphere and centered on the reversed PDL/G vector to achieve better measurement accuracy in a single test. Further, an upper bound of the mean of the Mueller matrix measurement error is derived when the measurement errors of output Stokes parameters independently and identically follow the ideal Gaussian distribution. This upper bound also shows that the statistically best Mueller matrix measurement accuracy can be obtained when the three input SOPs have the same relationship mentioned above. Simulation results confirm the validity of the theoretical findings.

© 2009 OSA

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  1. H. Dong, Y. D. Gong, V. Paulose, P. Shum, and M. Olivo, “Effect of input states of polarization on the measurement error of Mueller matrix in a system having small polarization-dependent loss or gain,” Opt. Express 17(15), 13017–13030 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-13017 .
    [CrossRef]
  2. N. Gisin and B. Huttner, “Combined effects of polarization mode dispersion and polarization dependent loss in optical fibers,” Opt. Commun. 142(1-3), 119–125 (1997).
    [CrossRef]
  3. K. Kikushima, K. Suto, H. Yoshinaga, and E. Yoneda, “Polarization dependent distortion in AM-SCM video transmission systems,” IEEE J. Lightwave Technol. 12(4), 650–657 (1994).
    [CrossRef]
  4. E. Lichtmann, “Performance degradation due to polarization dependent gain and loss in lightwave systems with optical amplifiers,” IEEE Photon. Technol. Lett. 5, 1969–1970 (1993).
  5. B. Huttner and N. Gisin, “Anomalous pulse spreading in birefringent optical fibers with polarization-dependent losses,” Opt. Lett. 22(8), 504–506 (1997).
    [CrossRef]
  6. H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Generalized Mueller matrix method for polarization mode dispersion measurement in a system with polarization-dependent loss or gain,” Opt. Express 14(12), 5067–5072 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5067 .
    [CrossRef]
  7. H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
    [CrossRef]
  8. A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
    [CrossRef]
  9. W. C. Waterhouse, “Do symmetric problems have symmetric solutions?” Am. Math. Mon. 90(6), 378–387 (1983).
    [CrossRef]
  10. H. Dong, J. Q. Zhou, M. Yan, P. Shum, L. Ma, Y. D. Gong, and C. Q. Wu, “Quasi-monochromatic fiber depolarizer and its application to polarization-dependent loss measurement,” Opt. Lett. 31(7), 876–878 (2006).
    [CrossRef]
  11. H. Dong, P. Shum, Y. D. Gong, M. Yan, J. Q. Zhou, and C. Q. Wu, “Virtual generalized Mueller matrix method for measurement of complex polarization-mode dispersion vector in optical fibers,” IEEE Photon. Technol. Lett. 19(1), 27–29 (2007).
    [CrossRef]
  12. E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).
  13. H. Dong, Y. D. Gong, V. Paulose, and M. H. Hong, “Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy,” Opt. Commun. 282(18), 3671–3675 (2009).
    [CrossRef]
  14. M. Reimer and D. Yevick, “Least-squares analysis of the Mueller matrix,” Opt. Lett. 31(16), 2399–2401 (2006).
    [CrossRef]

2009 (2)

2007 (2)

H. Dong, P. Shum, Y. D. Gong, M. Yan, J. Q. Zhou, and C. Q. Wu, “Virtual generalized Mueller matrix method for measurement of complex polarization-mode dispersion vector in optical fibers,” IEEE Photon. Technol. Lett. 19(1), 27–29 (2007).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
[CrossRef]

2006 (3)

2005 (1)

E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).

1997 (2)

B. Huttner and N. Gisin, “Anomalous pulse spreading in birefringent optical fibers with polarization-dependent losses,” Opt. Lett. 22(8), 504–506 (1997).
[CrossRef]

N. Gisin and B. Huttner, “Combined effects of polarization mode dispersion and polarization dependent loss in optical fibers,” Opt. Commun. 142(1-3), 119–125 (1997).
[CrossRef]

1995 (1)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
[CrossRef]

1994 (1)

K. Kikushima, K. Suto, H. Yoshinaga, and E. Yoneda, “Polarization dependent distortion in AM-SCM video transmission systems,” IEEE J. Lightwave Technol. 12(4), 650–657 (1994).
[CrossRef]

1993 (1)

E. Lichtmann, “Performance degradation due to polarization dependent gain and loss in lightwave systems with optical amplifiers,” IEEE Photon. Technol. Lett. 5, 1969–1970 (1993).

1983 (1)

W. C. Waterhouse, “Do symmetric problems have symmetric solutions?” Am. Math. Mon. 90(6), 378–387 (1983).
[CrossRef]

Ambirajan, A.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
[CrossRef]

Castro-Camus, E.

E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).

Dong, H.

H. Dong, Y. D. Gong, V. Paulose, P. Shum, and M. Olivo, “Effect of input states of polarization on the measurement error of Mueller matrix in a system having small polarization-dependent loss or gain,” Opt. Express 17(15), 13017–13030 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-13017 .
[CrossRef]

H. Dong, Y. D. Gong, V. Paulose, and M. H. Hong, “Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy,” Opt. Commun. 282(18), 3671–3675 (2009).
[CrossRef]

H. Dong, P. Shum, Y. D. Gong, M. Yan, J. Q. Zhou, and C. Q. Wu, “Virtual generalized Mueller matrix method for measurement of complex polarization-mode dispersion vector in optical fibers,” IEEE Photon. Technol. Lett. 19(1), 27–29 (2007).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Generalized Mueller matrix method for polarization mode dispersion measurement in a system with polarization-dependent loss or gain,” Opt. Express 14(12), 5067–5072 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5067 .
[CrossRef]

H. Dong, J. Q. Zhou, M. Yan, P. Shum, L. Ma, Y. D. Gong, and C. Q. Wu, “Quasi-monochromatic fiber depolarizer and its application to polarization-dependent loss measurement,” Opt. Lett. 31(7), 876–878 (2006).
[CrossRef]

Fraser, M. D.

E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).

Gisin, N.

N. Gisin and B. Huttner, “Combined effects of polarization mode dispersion and polarization dependent loss in optical fibers,” Opt. Commun. 142(1-3), 119–125 (1997).
[CrossRef]

B. Huttner and N. Gisin, “Anomalous pulse spreading in birefringent optical fibers with polarization-dependent losses,” Opt. Lett. 22(8), 504–506 (1997).
[CrossRef]

Gong, Y. D.

H. Dong, Y. D. Gong, V. Paulose, P. Shum, and M. Olivo, “Effect of input states of polarization on the measurement error of Mueller matrix in a system having small polarization-dependent loss or gain,” Opt. Express 17(15), 13017–13030 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-13017 .
[CrossRef]

H. Dong, Y. D. Gong, V. Paulose, and M. H. Hong, “Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy,” Opt. Commun. 282(18), 3671–3675 (2009).
[CrossRef]

H. Dong, P. Shum, Y. D. Gong, M. Yan, J. Q. Zhou, and C. Q. Wu, “Virtual generalized Mueller matrix method for measurement of complex polarization-mode dispersion vector in optical fibers,” IEEE Photon. Technol. Lett. 19(1), 27–29 (2007).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Generalized Mueller matrix method for polarization mode dispersion measurement in a system with polarization-dependent loss or gain,” Opt. Express 14(12), 5067–5072 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5067 .
[CrossRef]

H. Dong, J. Q. Zhou, M. Yan, P. Shum, L. Ma, Y. D. Gong, and C. Q. Wu, “Quasi-monochromatic fiber depolarizer and its application to polarization-dependent loss measurement,” Opt. Lett. 31(7), 876–878 (2006).
[CrossRef]

Hong, M. H.

H. Dong, Y. D. Gong, V. Paulose, and M. H. Hong, “Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy,” Opt. Commun. 282(18), 3671–3675 (2009).
[CrossRef]

Huttner, B.

N. Gisin and B. Huttner, “Combined effects of polarization mode dispersion and polarization dependent loss in optical fibers,” Opt. Commun. 142(1-3), 119–125 (1997).
[CrossRef]

B. Huttner and N. Gisin, “Anomalous pulse spreading in birefringent optical fibers with polarization-dependent losses,” Opt. Lett. 22(8), 504–506 (1997).
[CrossRef]

Jagadish, C.

E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).

Johnston, M. B.

E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).

Kikushima, K.

K. Kikushima, K. Suto, H. Yoshinaga, and E. Yoneda, “Polarization dependent distortion in AM-SCM video transmission systems,” IEEE J. Lightwave Technol. 12(4), 650–657 (1994).
[CrossRef]

Lichtmann, E.

E. Lichtmann, “Performance degradation due to polarization dependent gain and loss in lightwave systems with optical amplifiers,” IEEE Photon. Technol. Lett. 5, 1969–1970 (1993).

Lloyd-Hughes, J.

E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).

Look, D. C.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
[CrossRef]

Ma, L.

Ning, G. X.

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Generalized Mueller matrix method for polarization mode dispersion measurement in a system with polarization-dependent loss or gain,” Opt. Express 14(12), 5067–5072 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5067 .
[CrossRef]

Olivo, M.

Paulose, V.

Reimer, M.

Shum, P.

Suto, K.

K. Kikushima, K. Suto, H. Yoshinaga, and E. Yoneda, “Polarization dependent distortion in AM-SCM video transmission systems,” IEEE J. Lightwave Technol. 12(4), 650–657 (1994).
[CrossRef]

Tan, H. H.

E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).

Waterhouse, W. C.

W. C. Waterhouse, “Do symmetric problems have symmetric solutions?” Am. Math. Mon. 90(6), 378–387 (1983).
[CrossRef]

Wu, C. Q.

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
[CrossRef]

H. Dong, P. Shum, Y. D. Gong, M. Yan, J. Q. Zhou, and C. Q. Wu, “Virtual generalized Mueller matrix method for measurement of complex polarization-mode dispersion vector in optical fibers,” IEEE Photon. Technol. Lett. 19(1), 27–29 (2007).
[CrossRef]

H. Dong, J. Q. Zhou, M. Yan, P. Shum, L. Ma, Y. D. Gong, and C. Q. Wu, “Quasi-monochromatic fiber depolarizer and its application to polarization-dependent loss measurement,” Opt. Lett. 31(7), 876–878 (2006).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Generalized Mueller matrix method for polarization mode dispersion measurement in a system with polarization-dependent loss or gain,” Opt. Express 14(12), 5067–5072 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5067 .
[CrossRef]

Yan, M.

H. Dong, P. Shum, Y. D. Gong, M. Yan, J. Q. Zhou, and C. Q. Wu, “Virtual generalized Mueller matrix method for measurement of complex polarization-mode dispersion vector in optical fibers,” IEEE Photon. Technol. Lett. 19(1), 27–29 (2007).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Generalized Mueller matrix method for polarization mode dispersion measurement in a system with polarization-dependent loss or gain,” Opt. Express 14(12), 5067–5072 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5067 .
[CrossRef]

H. Dong, J. Q. Zhou, M. Yan, P. Shum, L. Ma, Y. D. Gong, and C. Q. Wu, “Quasi-monochromatic fiber depolarizer and its application to polarization-dependent loss measurement,” Opt. Lett. 31(7), 876–878 (2006).
[CrossRef]

Yevick, D.

Yoneda, E.

K. Kikushima, K. Suto, H. Yoshinaga, and E. Yoneda, “Polarization dependent distortion in AM-SCM video transmission systems,” IEEE J. Lightwave Technol. 12(4), 650–657 (1994).
[CrossRef]

Yoshinaga, H.

K. Kikushima, K. Suto, H. Yoshinaga, and E. Yoneda, “Polarization dependent distortion in AM-SCM video transmission systems,” IEEE J. Lightwave Technol. 12(4), 650–657 (1994).
[CrossRef]

Zhou, J. Q.

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
[CrossRef]

H. Dong, P. Shum, Y. D. Gong, M. Yan, J. Q. Zhou, and C. Q. Wu, “Virtual generalized Mueller matrix method for measurement of complex polarization-mode dispersion vector in optical fibers,” IEEE Photon. Technol. Lett. 19(1), 27–29 (2007).
[CrossRef]

H. Dong, J. Q. Zhou, M. Yan, P. Shum, L. Ma, Y. D. Gong, and C. Q. Wu, “Quasi-monochromatic fiber depolarizer and its application to polarization-dependent loss measurement,” Opt. Lett. 31(7), 876–878 (2006).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Generalized Mueller matrix method for polarization mode dispersion measurement in a system with polarization-dependent loss or gain,” Opt. Express 14(12), 5067–5072 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5067 .
[CrossRef]

Am. Math. Mon. (1)

W. C. Waterhouse, “Do symmetric problems have symmetric solutions?” Am. Math. Mon. 90(6), 378–387 (1983).
[CrossRef]

IEEE J. Lightwave Technol. (1)

K. Kikushima, K. Suto, H. Yoshinaga, and E. Yoneda, “Polarization dependent distortion in AM-SCM video transmission systems,” IEEE J. Lightwave Technol. 12(4), 650–657 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

E. Lichtmann, “Performance degradation due to polarization dependent gain and loss in lightwave systems with optical amplifiers,” IEEE Photon. Technol. Lett. 5, 1969–1970 (1993).

H. Dong, P. Shum, Y. D. Gong, M. Yan, J. Q. Zhou, and C. Q. Wu, “Virtual generalized Mueller matrix method for measurement of complex polarization-mode dispersion vector in optical fibers,” IEEE Photon. Technol. Lett. 19(1), 27–29 (2007).
[CrossRef]

Opt. Commun. (3)

H. Dong, Y. D. Gong, V. Paulose, and M. H. Hong, “Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy,” Opt. Commun. 282(18), 3671–3675 (2009).
[CrossRef]

H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Measurement of Mueller matrix for an optical fiber system with birefringence and polarization-dependent loss or gain,” Opt. Commun. 274(1), 116–123 (2007).
[CrossRef]

N. Gisin and B. Huttner, “Combined effects of polarization mode dispersion and polarization dependent loss in optical fibers,” Opt. Commun. 142(1-3), 119–125 (1997).
[CrossRef]

Opt. Eng. (1)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Proc. SPIE (1)

E. Castro-Camus, J. Lloyd-Hughes, M. D. Fraser, H. H. Tan, C. Jagadish, and M. B. Johnston, “Detecting the full polarization state of terahertz transients,” Proc. SPIE 6120, 61200Q (2005).

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